Is it for the PC or for the MAC?
What kind of system do you have? XP, Vista, 7?
You were able to install the game fine?
Are there any error messages? How do you close it, when it freezes up with a black screen?
What kind of video card do you have? What resolution are you using?
When it goes to a black screen, if you press Z several times for 20-30 seconds does anything happen (any sounds perhaps)?
Is it a laptop or a desktop (or something else)?
Have you tried to change the resolution to something small, and then run the game?
Can you alt-tab out of the game when it loads that black screen, and then come back?
Hmm......... what else...........................
Also, have you tried installing it on another computer just to see if it works elsewhere?
BTW :
HAve you tried posting this on the official forum for CaveStory+?
http://forums.steampowered.com/forums/forumdisplay.php?f=1281
EDIT:
Hmm... uh try this :
Download the msvcr100.dll (It comes in a ZIP file, so extract that) [Not the dll fixer thing]
http://www.dll-files.com/dllindex/dll-files.shtml?msvcr100
And put it into your Cave Story+ application directory.
(My Cave Story+ directory was : C:\Program Files\Steam\steamapps\common\cave story+ )
Throw that .dll in there if it doesn't already exist.
Now open Steam and try hitting play again... Any luck? (It's worth a shot)